Geometry and Its Interdisciplinary Applications: A Comprehensive Review

Abstract

Geometry is one of the oldest and most fundamental branches of mathematics, evolving from practical land measurement techniques into a sophisticated and interdisciplinary field with applications in engineering, physics, computer science, medicine, architecture, and environmental sciences. This review paper explores the historical development, major branches, and modern applications of geometry, highlighting its significance in solving real-world problems. Special attention is given to Euclidean geometry, analytic geometry, differential geometry, computational geometry, and fractal geometry. The paper also discusses case studies related to bridge design and computer graphics, illustrating the practical implementation of geometric principles. Furthermore, current research gaps and future interdisciplinary opportunities are identified. The review demonstrates that geometry remains a cornerstone of scientific innovation and technological advancement.